Problem: Simplify the following expression: $ z = \dfrac{9}{r + 4} + \dfrac{-6}{5} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{9}{r + 4} \times \dfrac{5}{5} = \dfrac{45}{5r + 20} $ Multiply the second expression by $\dfrac{r + 4}{r + 4}$ $ \dfrac{-6}{5} \times \dfrac{r + 4}{r + 4} = \dfrac{-6r - 24}{5r + 20} $ Therefore $ z = \dfrac{45}{5r + 20} + \dfrac{-6r - 24}{5r + 20} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{45 - 6r - 24}{5r + 20} $ $z = \dfrac{-6r + 21}{5r + 20}$